If A = begin{bmatrix} 2 & 0 & 0 0 & 3 & 0 0 | vedclass

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(A) Given $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$, then $A^2 = \begin{bmatrix} 2^2 & 0 & 0 \ 0 & 3^2 & 0 \ 0 & 0 & 4

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$\begin{bmatrix} 5 & 0 & 0 \ 0 & 13 & 0 \ 0 & 0 & 25 \end{bmatrix}$

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(A) Given $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$, then $A^2 = \begin{bmatrix} 2^2 & 0 & 0 \ 0 & 3^2 & 0 \ 0 & 0 & 4^2 \end{bmatrix} = \begin{bmatrix} 4 & 0 & 0 \ 0 & 9 & 0 \ 0 & 0 & 16 \end{bmatrix}$.Given $B = \begin{bmatrix} 1 & 0 & 0 \ 0 & -2 & 0 \ 0 & 0 & -3 \end{bmatrix}$, then $B^2 = \begin{bmatrix} 1^2 & 0 & 0 \ 0 & (-2)^2 & 0 \ 0 & 0 & (-3)^2 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 9 \end{bmatrix}$.Therefore, $A^2 + B^2 = \begin{bmatrix} 4+1 & 0 & 0 \ 0 & 9+4 & 0 \ 0 & 0 & 16+9 \end{bmatrix} = \begin{bmatrix} 5 & 0 & 0 \ 0 & 13 & 0 \ 0 & 0 & 25 \end{bmatrix}$.

If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix}$, then $A^2 + B^2=$ . . . . . . .

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